Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x - 6$ and $ JT = 4x + 29$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x - 6} = {4x + 29}$ Solve for $x$ $ 5x = 35$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({7}) - 6$ $ JT = 4({7}) + 29$ $ CJ = 63 - 6$ $ JT = 28 + 29$ $ CJ = 57$ $ JT = 57$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {57} + {57}$ $ CT = 114$